Nuclear Zeeman effect

The energy of a nuclear dipole moment in an external magnetic field, B, is given by 

FIGURE 1.35 Precession of nuclear dipole magnetic moment. 

The Physical Chemistry of Materials Energy and Environmental Applications 

FIGURE 1.36 Energy separation between nuclear spin states for a system immersed in an external magnetic field. 

Transitions between the two energy states, spin up and spin down, can occur by absorption or emission of electromagnetic radiation of frequency, vL, which is given by the Larmor equation [44]  

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A nucleus in a state with spin quantum number 7 > 0 will interact with a magnetic field by means of its magnetic dipole moment p. This magnetic dipole interaction or nuclear Zeeman effect may be described by the Hamiltonian... 

Fig. 4.9 Magnetic dipole splitting (nuclear Zeeman effect) in pe and resultant Mossbauer spectrum (schematic). The mean energy of the nuclear states is shifted by the electric monopole interaction which gives rise to the isomer shift 5. Afi. g = Sg/tN and A M,e = refer to the...

The nuclear Zeeman effect is not a very strong interaction as compared to electric quadrupole splitting because of the relatively weak nuclear magneton. A field of B... 

Au dissolved in ferromagnetic hosts of Fe, Co, Ni as sources versus Au metal absorber Nuclear Zeeman effect in Au atoms, super-transferred hf fields, // at Au sites... 

Many other diatomic molecules with1X ground states have been studied by molecular beam magnetic resonance. Where magnetic nuclei are present, magnetic focusing is based upon the nuclear Zeeman effects. This is the case with 15N2 for which the... 

As we have said, a nucleus with nuclear spin 7 adopts 27 + 1 nondegenerate spin orientations in a magnetic field. The states separate in energy, with the largest positive m value corresponding to the lowest energy (most stable) state. It is this separation of states in a magnetic field that is the essence of the nuclear Zeeman effect. 

Figure 2.3. Nuclear Zeeman effect, (a) A nucleus with / = 4. (b) A nucleus with / = 1. The arrow beside each spin state line indicates the orientation of the magnetic moment in a vertical magnetic field.

Magnetic Hyperfine Interaction (MHI). This interaction arises from the interaction of the nuclear dipole moment with a magnetic field due to the atom s own electrons. The nuclear Zeeman effect may be described by the Hamiltonian (15)... 

In an exterior magnetic field, the torque on the magnetic moment of the spinning nucleus, /aligning force of the intramolecular potential. The corresponding potential energy (nuclear Zeeman effect) is given by ... 

Thus, for 7 = J, the energy levels are represented in Fig. 3. This is the nuclear Zeeman effect and is the basis of nuclear magnetic resonance. 

The third important hyperfine interaction is the nuclear Zeeman effect [20]. This will occur if there is a magnetic field at the nucleus. The magnetic field... 

Magnetic dipole interaction, detectable as a line sphtting (nuclear Zeeman effect). 

To analyze the recorded spectra, the spectrometer needs to be calibrated. The three main calibration parameters are the velocity scale, the center point of the spectrum and the nonlinearity of the velocity/time profile of the oscillation compared to a standard reference. The calibration is performed using a spectrum recorded from an a-iron foil at room temperature using the well defined line positions of the sextet from a-iron, which occur at 5.312mms , 3.076mms , and 0.840mms The center of this a-iron spectrum at room temperature is taken as the reference point (0.0 nun s ) for isomer shift values of sample spectra. The typical Mossbauer spectrum of the 14.4 keV transition of Fe in natural iron (Fig. 4.10) represents a simple example of pure nuclear Zeeman effect. Because of the cubic symmetry of the iron lattice, there is no quadrupole shift of the nuclear energy levels. The relative intensities of the six magnetic dipole transitions are... 

Magnetic Dipole Interaction Magnetic Splitting (Nuclear Zeeman Effect)... 

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